The state of nonrelativistic quantum system in a relativistic reference frame

TL;DR

This paper demonstrates that the internal nonrelativistic state of a bound quantum system remains unchanged under Lorentz transformations, challenging the common expectation of Lorentz contraction for such states.

Contribution

It shows that a spherically symmetric nonrelativistic internal state is invariant under Lorentz boosts, with implications for modeling hadron structures in relativistic frames.

Findings

Internal states are unchanged during frame transitions.

Spherical symmetry is preserved in all reference frames.

No Lorentz contraction occurs for the internal state.

Abstract

We consider the problem of internal particle state transformation, which is a bound state of several constituents, from the particle's rest frame to the system in which this particle is relativistic. It is assumed that in the rest frame of the composite particle, its internal state can be considered in the nonrelativistic approximation. It is shown, that this internal state is unchanged during the transition from one reference frame to another. Namely, given the particle is spherically symmetric in the rest frame, it remains spherically symmetric in any other reference frame, and does not undergo Lorentz contraction along the direction of motion of moving reference frame with respect to the rest frame. We discuss a possible application of these results to the description of hadron-hadron scattering, considering hadrons as a bound states of quarks.